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Meaning of Pi 1 The Meaning & Use of Pi by Joseph A. Castellano, Ph.D.

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Presentation on theme: "Meaning of Pi 1 The Meaning & Use of Pi by Joseph A. Castellano, Ph.D."— Presentation transcript:

1 Meaning of Pi 1 The Meaning & Use of Pi by Joseph A. Castellano, Ph.D.

2 Meaning of Pi 2 How Pi (π) is Derived Take a circle of string, 1 meter in diameter, cut it, stretch it out and measure its length: d = 1 m L = m π = The length of the string is m. The circumference of every circle is always times its diameter. This constant is known as pi and denoted by the Greek letter, π.

3 Meaning of Pi 3 How Pi (π) is Used To calculate C, the circumference of a circle using the diameter, d or the radius, r: C. rr d d = 2 r C = π 2 r C = π d or

4 Meaning of Pi 4 How Pi (π) is Used To calculate A, the area of a circle using the radius, r:. r A = π r 2

5 Meaning of Pi 5 How Pi (π) is Used To calculate A, the area of a circle using the diameter, d:. d A = π d 2 ___ ___ 4

6 Meaning of Pi 6 How Pi (π) is Used To calculate the surface area of a sphere As, using the radius, r: As = 4 π r 2. r

7 Meaning of Pi 7 How Pi (π) is Used To calculate the volume of a sphere Vs, using the radius, r, or the diameter, d: Vs = 4/3 π r 3 or Vs = 1/6 π d 3. r

8 Meaning of Pi 8 Summary The circumference of a circle is times its diameter. This value is defined by the Greek letter π (Pi) The circumference of a circle, C is equal to: C = d π or C = 2 r π

9 Meaning of Pi 9 Summary The area of a circle, A, is equal to: The surface area of a sphere, As, is equal to: The volume inside a sphere, Vs, is equal to: As = 4 π r 2 Vs = 4/3 π r 3 or Vs = 1/6 π d 3 or A = (π d 2 )/4 A = π r 2


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